luck (noun)
a: a force that brings good fortune or adversity
b: the events or circumstances that operate for or against an individual

Chad and Niv brought up some points in the comments to this post, and then I discussed things a bit further with them (in person in the case of Chad!). The biggest problem with that post is that i just basically categorized events as being luckly/unlucky without any real definition of the term. Well, I guess I was using the above definition, but there is way too much room to interpret how that may apply to baseball. In addition, there is a big distinction to be made between luck on an individual play and luck over the course of an entire game – I was confusing the two in a bit in that post, and will try to be a bit more distinct here.

Let us take a step back first and think about a game which is much more simple than baseball: darts. Let’s say you hit a bullseye; if you were to recreate the same exact physiological motion from the same exact location (location meaning physical structure and placement within that structure) and environment (same noise level/people moving around you) with the same exact grip that you used to hit that bullseye, you would with 100% certainty hit it again. You only depend on your own talents for an individual throw, so there is no luck involved whatsoever. Because the game itself is practically unchanging (you might have to aim for a 17 instead of the bullseye, but you are still the same distance away and using the same darts) and is turn-based (as opposed to interactive between the various players), you aren’t really competing against someone else as you play but rather you are competing against yourself relative to someone else competing against themselves (assuming you are not playing with teams). Your own performance can be neither lucky or unlucky; rather, you as an individual reap what you sow. However, because you yourself have no control over the performance of your opponent, the final outcome of the game may be lucky or unlucky based on how they perform relative to what is expected of them: if they hit numbers more quickly than they are expected to then you are unlucky, and if they hit numbers less quickly than they are expected to then you are lucky.

A game that adds an additional layer of complexity to darts is pool: it is turn-based, played in a climate-controlled environment, and uses a consistent set of equipment. However, unlike in darts the placement of the balls creates an infinite set of possible situations in which one can face. A player can repeat the same motion given the same situation and get the same result as in darts – therefore there is still no luck involved on an individual shot – but unlike darts they must be prepared to deal with any number of situations. Since these situations can range in difficulty from simple to impossible, it is possible for one player to face a much easier set of shots than the other. However, since leaving your opponent difficult shots is a skill in itself, this must be taken into account when trying to determine the role of luck. Therefore, one is lucky over an entire game of pool if they face easier shots than expected given opponent quality and/or have more opportunities at shots given opponent quality (due to unexpected misses by the opposition).

Golf seems to be a mixture of these two games to me – while the required shots change significantly over the course of a hole, each player is responsible for where their ball lies and plays no role in shots of the of their opponents. However, weather is brought into play for golf – an unexpected gust of wind blowing a shot off the green, for instance – and this means there is the potential for a slight bit luck on an individual shot (I would say this is slightly more common than someone dropping a glass while you are about to take your shot in pool, but overall it is pretty similar).

However, over the course of an entire tournament golf is a bit different than the other two games due to the fact that: 1) there are many more holes of golf in a tournament, reducing the volatility of the performance of each individual competitor; 2) there are many more competitors playing, reducing the volatility of the performance of all competitors in aggregate; and 3) the weather can change, potentially creating different conditions for the various competitors. Points 1 and 2 lead to the conclusion that, for the most part, you can have a pretty good idea about how the tournament scores will be distributed before it even starts. However, these may be affected by point 3. Also, while the overall distribution of scores are what matter for a tournament, when it comes to winning it is those scores on the end of the distribution that matter, and these will still be a bit volatile. Nevertheless, one can be considered to be lucky over an entire golf tournament if their competitors have performed worse than expected given the weather which they have faced and/or if the competitor has played in more favorable weather conditions than the rest of the competitors overall.

Finally, baseball. Let’s skip over the whole pitch selection part of the equation (which deserves a whole different post in itself) and just deal with balls in play. If you throw the dart/hit the pool ball/hit the golf ball where you want to throw/hit/hit it, then on an individual basis there is very little luck involved (except for dropped glasses/wind gusts). In baseball, however, there is no such guarantee. If you hit the ball exactly where you want to hit it in play, there is some non-zero probability it will turn into an out. And due to the nature of the game, is is much more difficult to hit a baseball exactly where you want it than to throw a dart/hit a pool ball/hit a golf ball exactly where you want it. That means that, on an individual play in baseball, there is some luck involved. A batter is lucky on a single play if the value of the outcome of the play exceeds the expected value of that ball in play. As samples increase in size this luck should even out somewhat – over a career there should be very little luck, but over the course of a game it certainly still plays a role in the outcome.

Note: I extracted some of this post in its original form for this so just imagine this as all being a prequel to that post.

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